This is a good question and I can see your confusion. The sentence is not written very well.

First, we need to make two corrections. The fourth word should read "gets;" we can even change that word to "obtains," to make the meaning of the sentence even clearer. Second, to make the sentence even clearer we should add a relative pronoun before the word "recently," to create an adjectival clause. If we do this, the sentence would read:

"The Rizal monument gets / obtains a Manhattan like backdrop in an artist's perspective, which was recently released by property developer, DMCI, to defend its controversial Torre de Manila condominium project in Manila."

Now based on this sentence, we can say that the verb is "gets." The direct object is "a Manhattan like backdrop." The prepositional phrase is "in an artist's perspective." The rest of the sentence is a adjectival clause.

The whole predicate is: "a Manhattan like backdrop in an artist's perspective, which was recently released by property developer, DMCI, to defend its controversial Torre de Manila condominium project in Manila."

If we parse this sentence even further, the adjectival clause has a verb "was released," and what follows is the predicate of the adjectival clause.